Sub-Quadratic Decoding of One-Point Hermitian Codes

We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power decodi...

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Vydáno v:	IEEE transactions on information theory Ročník 61; číslo 6; s. 3225 - 3240
Hlavní autoři:	Nielsen, Johan S. R., Beelen, Peter
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 01.06.2015 The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers
Témata:	AG codes Algebra Algorithms Coding theory Complexity theory Computer Science Decoding Electronics Guruswami-Sudan Hermitian codes Indexes Information Theory Interpolation list decoding Minimization Polynomials Power decoding power decoding Guruswami–Sudan Hermitian codes AG codes list decoding Power decoding Guruswami-Sudan
ISSN:	0018-9448, 1557-9654
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Popis
Shrnutí:	We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the matrix minimization algorithms from computer algebra, yielding similar asymptotic complexities.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2015.2424415